Oscarlevin: Created page with "I have a d-digit positive integer where each digit from 1 to d appears exactly once, and in which each digit (except for the leftmost) differs from one further to the lef..."

2013-09-02T15:12:00Z

Created page with "I have a d-digit positive integer where *each digit from 1 to d appears exactly once, and in which *each digit (except for the leftmost) differs from one further to the lef..."

New page

I have a d-digit positive integer where

*each digit from 1 to d appears exactly once,

and in which

*each digit (except for the leftmost) differs from one further to the left by +1 or -1.

For example, if d = 3, the only numbers satisfying the conditions are, in increasing order, 123, 213, 231 and 321.
Find a formula in terms of d for the number of integers satisfying these conditions.

(More difficult problem: Instead of the first condition, suppose I only tell you that the d digits are distinct. Now how many integers satisfy the conditions?)

{{Bpow}}

Draft:Bpow35 - Revision history

Oscarlevin: Created page with "I have a d-digit positive integer where *each digit from 1 to d appears exactly once, and in which *each digit (except for the leftmost) differs from one further to the lef..."

Oscarlevin: Created page with "I have a d-digit positive integer where each digit from 1 to d appears exactly once, and in which each digit (except for the leftmost) differs from one further to the lef..."